The present invention relates to piezoelectric vibrators employing aluminum nitride as piezoelectric material, and it also relates to piezoelectric filters using the piezoelectric vibrator.
Piezoelectric vibration devices, which use bulk wave propagating through a solid body, include a piezoelectric vibrator to be used as a clock source of various electronic apparatuses and a piezoelectric filter to be used for extracting a frequency in a communication device. Recently a higher frequency has been used in those piezoelectric vibration devices. Thickness sliding vibration or thickness longitudinal vibration is used as primary vibration, and an energy confinement phenomenon, which is particularly effective for suppressing undesired vibrations and for holding the devices with ease, is often used in the piezoelectric vibration devices. The energy confinement phenomenon is to confine vibration energy only underneath an excitation electrode in the following case: The excitation electrode is formed at a portion on a partial principal plane of a vibrating element under the condition that a specific vibration mode such as thickness sliding vibration or thickness longitudinal vibration is used in a specific piezoelectric material. This phenomenon is analyzed exhaustively by Messrs. Shockley and Onoe. The energy confinement phenomenon is described hereinafter with reference to a sectional view of vibrating element 100 shown in FIG. 14. Assume that a cut-off frequency at a place of excitation electrode 101 is fo, and a cut-off frequency at a non-electrode section is foxe2x80x2. Vibration energy propagates free from regulations when the frequency is higher than foxe2x80x2, and does not form standing wave even underneath excitation electrode 101. On the other hand, when the frequency is less than foxe2x80x2 and greater than fo, the vibration energy propagates free from regulations in a place of excitation electrode 101; however, the energy attenuates exponentially in the non-electrode section, as shown in FIG. 14. Vibration displacement thus becomes smaller as it approaches to the ends of vibrating element 100. As a result, the vibration energy concentrates on the vicinity of excitation electrode 101. At both the ends of vibrating element 100, the vibration displacement is small enough to suppress reflecting waves which occur at both the ends, so that the characteristics of the primary vibration, namely thickness longitudinal vibration or thickness sliding vibration, can be improved.
Uses of the energy confinement phenomenon, however, hardly suppress undesired resonance that is caused by a length or a width of the vibrating element. Therefore, the dimensions of the vibrating element need to be appropriate so that undesired resonance cannot occur at the vicinity of the resonance frequency of the primary vibration. For instance, Japanese Patent Gazette No. 1577973 teaches as follows: a strip-vibrator, of which primary vibration is thickness sliding vibration, uses X-cut of lithium tantalate, and when the following relation is satisfied, a frequency of undesired resonance due to a width of a vibrating element is away from the principal frequency resonance:
1.35xe2x89xa6W/Hxe2x89xa63.0, or
3.8xe2x89xa6W/Hxe2x89xa65.0,
where W is width of the vibrating element, and H is thickness of the vibrating element. As a result, the better characteristic can be obtained.
However, in the case of a piezoelectric vibrator using thickness sliding vibration as the primary vibration, aluminum nitride as piezoelectric material, and a polarization direction directed along the longitudinal direction of the vibrating element, the following problem occurs. No definite dimensions are available for moving away the undesired resonance, caused by the width of vibrating element, from the resonance frequency of the primary vibration.
A piezoelectric vibrator uses aluminum nitride as piezoelectric material, thickness sliding vibration as the primary vibration, and a polarization direction directed along the longitudinal direction of its vibrating element. Dimensions of the vibrating element are defined as follows:
2.0xe2x89xa6W/Hxe2x89xa64.0 or 4.3xe2x89xa6W/Hxe2x89xa65.7 or 6.2xe2x89xa6W/Hxe2x89xa67.8 or 8.2xe2x89xa6W/Hxe2x89xa69.8, where W is a width of the vibrating element, and H is a thickness of the vibrating element.